1. **Stating the problem:** We are given that the measure of angle 2 is $m\angle 2 = 5x + 4$ degrees. 2. **Understanding the figure and given information:** The figure shows two triangles sharing a vertex with angles labeled. One triangle has an angle of 61° and the shared angle is labeled 1. Angle 2 is adjacent to angle 1 in the right triangle. 3. **Using the triangle angle sum property:** The sum of the interior angles of a triangle is always 180°. 4. **Setting up the equation:** From the handwritten notes, it appears the equation used is $5x + 36 = 180$ which likely comes from summing angles in one of the triangles. 5. **Solving for $x$:** $$ 5x + 36 = 180 $$ Subtract 36 from both sides: $$ 5x + \cancel{36} - \cancel{36} = 180 - 36 $$ $$ 5x = 144 $$ Divide both sides by 5: $$ \frac{5x}{\cancel{5}} = \frac{144}{\cancel{5}} $$ $$ x = \frac{144}{5} = 28.8 $$ 6. **Finding the measure of angle 2:** Substitute $x=28.8$ back into $m\angle 2 = 5x + 4$: $$ m\angle 2 = 5(28.8) + 4 = 144 + 4 = 148\degree $$ **Final answer:** The measure of angle 2 is $148\degree$.